Conventional magnetic resonance imaging (MRI) can produce relaxation parameter maps. The relaxation parameter maps are produced from nuclear magnetic resonance (NMR) signals produced in response to NMR excitation. The NMR signals may be produced by sensitizing an MRI signal to either T1 (spin-lattice) relaxation or T2 (spin-spin) relaxation, waiting a variable amount of time, and then collecting the resulting NMR signals. Conventionally, single voxels have been assumed to comprise only a single tissue type having a single T1 value and a single T2 value. In this conventional approach, the acquired signal time course follows an exponential recovery or decay. The acquired signal time course may thus be fit to an exponential model to calculate a value for the relaxation parameter (e.g., T1, T2) in the voxel. This operation may be performed for each voxel when producing a relaxation parameter map. Conventional quantitative relaxation parameter map production requires a significant time to elapse between NMR excitation and NMR signal acquisition to sample the recovery or delay curves. For example, delays of up to several seconds are common in T1 mapping. This delay may make it difficult, if even possible at all, to distinguish signals from multiple compartments in a volume.
Conventional approaches that assume that a single voxel will produce a single exponential recovery or decay may be challenged when a voxel contains two different compartments having different relaxation characteristics or when a voxel has a single compartment that has two components that experience exchange. The approach may be challenged even further to account for different situations that produce different results. For example, when different compartments have no magnetic exchange between them, the relaxation signal may be bi-exponential. However, when different compartments have magnetic exchange between compartments, then the resulting signal evolution may follow a time course that is dictated by a mixture of the relaxation parameters. If the exchange is fast relative to the experiment, then the relaxation parameter value in the single voxel may be described according to:
            1              T                  1          ,          c                      =                            ρ          A                          T                      1            ,            A                              +                        ρ          B                          T                      1            ,            B                                or            1              T                  2          ,          c                      =                            ρ          A                          T                      2            ,            A                              +                        ρ          B                          T                      2            ,            B                              
where:                T1,A is the T1 value for the water in compartment A,        T2,A is the T2 value for the water in compartment A,        T1,B is the T1 value for the water in compartment B,        T2,B is the T2 value for the water in compartment B,        ρA is the relative volume fraction of compartment A, and        ρB is the relative volume fraction of compartment B.        
In conventional approaches, when the magnetic exchange between compartments is slower and occurs on a timescale on the same order of magnitude as the experimental time, then the exchange will affect the observed relaxation value. For example, in a conventional T1 mapping experiment, an exchange rate of approximately 8.3 s−1 between compartments with T1 and T2 values of 350 ms/1400 ms and 30 ms/120 ms, and relative volume fractions of 25% and 75% will produce an effective mono-exponential relaxation value of 1020 ms. The exchange rate of approximately 8.3 s−1 corresponds to a mean extracellular residence time of 120 ms. T1 and T2 values of 350 ms/1400 ms and 30 ms/120 ms and relative volume fractions of 25% and 75% are observed in myocardial tissue.
FIG. 1 illustrates a volume 190 having two compartments between which magnetic exchange occurs. A first volume 100 may be, for example, an extracellular volume and a second volume 110 may be, for example, an intracellular volume. The intracellular volume 110 and the extracellular volume 100 may be present in tissues including, for example, a myocardial tissue. Molecules, chemicals, or spins may move between the first volume 100 and the second volume 110 causing magnetization exchange between the two volumes. For example, water molecules 112 and 114 may move from the second volume 110 into the first volume 100 while water molecules 102 and 104 may move from the first volume 100 into the second volume 110.
Resonant species in extracellular volume 100 may have a first set of properties (e.g., T1extra, T2extra). Resonant species in intracellular volume 110 may have a second set of properties (e.g., T1intra, T2intra). Conventionally, MRI has been unable to distinguish T1intra from T1extra and thus a T1 signal from the entire volume 190 that included the intracellular volume 110 and the extracellular volume 100 may have been a combination of T1intra and T1extra. While the intracellular volume 110 is illustrated entirely inside the extracellular volume 100, other arrangements of sub-volumes are possible.
Characterizing resonant species using NMR can include identifying different properties of a resonant species (e.g., T1 spin-lattice relaxation, T2 spin-spin relaxation, proton density). Other properties like tissue types and super-position of attributes can also be identified using NMR signals. These properties and others may be identified simultaneously using magnetic resonance fingerprinting (MRF), which is described in Magnetic Resonance Fingerprinting, Ma D et al., Nature 2013:495, (7440):187-192.